Turns the cohomology of a space into a graded ring
In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree p and q to form a composite cocycle of degree p + q. This defines an associative (and distributive) graded commutative product operation in cohomology, turning the cohomology of a space X into a graded ring, H∗(X), called the cohomology ring. The cup product was introduced in work of J. W. Alexander, Eduard Čech and Hassler Whitney from 1935–1938, and, in full generality, by Samuel Eilenberg in 1944.
In mathematics, specifically in algebraic topology, the cupproduct is a method of adjoining two cocycles of degree p and q to form a composite cocycle...
calculus Tensor productProduct topology Cap productCupproduct Slant product Smash product Wedge sum (or wedge product) Internal product, in a monoidal...
{\mathcal {P}}({\mathcal {P}}(A\cup B))} where P {\displaystyle {\mathcal {P}}} denotes the power set. Then the Cartesian product of the sets A {\displaystyle...
function F ∘ f on X. The most important cohomology theories have a product, the cupproduct, which gives them a ring structure. Because of this feature, cohomology...
Single servings of the product are packaged in foam, plastic, or paper cups and are prepared by adding boiling water. The brand name Cup Noodle is also a registered...
X is a ring formed from the cohomology groups of X together with the cupproduct serving as the ring multiplication. Here 'cohomology' is usually understood...
well. While the cupproduct of ordinary cohomology describes how submanifolds of the manifold intersect each other, the quantum cupproduct of quantum cohomology...
with the interpretation of the cupproduct in terms of the Künneth formula, we can explain the existence of the cap product in the following way. Using CW...
algebra: the algebraic structure arising on the cochain level for the cupproduct Poincaré duality: swaps some of these Intersection theory: for a similar...
company Keurig Dr Pepper manufactures the machines. The main Keurig products are K-Cup pods, which are single-serve coffee containers; other beverage pods;...
curve C, then their wedge product is necessarily zero because C has only one complex dimension; consequently, the cupproduct of their cohomology classes...
the Massey product is a cohomology operation of higher order introduced in (Massey 1958), which generalizes the cupproduct. The Massey product was created...
In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result...
The cupproduct of two cocycles is again a cocycle, and the product of a coboundary with a cocycle (in either order) is a coboundary. The cupproduct operation...
flow." The EU legislated that "The product group ‘reusable menstrual cups’ shall comprise reusable flexible cups or barriers worn inside the body whose...
L\rightarrow 0\in \operatorname {Ext} ^{m}(L,M),} we form the Yoneda (cup) product ξ ⌣ ρ : 0 → N → E 0 → ⋯ → E n − 1 → F 0 → ⋯ → F m − 1 → L → 0 ∈ Ext m...
isomorphic (as graded rings), where the analogous product on singular cohomology is the cupproduct. For any smooth manifold M, let R _ {\textstyle {\underline...
hygiene products, including menstrual pads, tampons, pantyliners, menstrual cups, menstrual sponges and period panties. Feminine hygiene products also include...
product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product....
A disposable (also called disposable product) is a product designed for a single use after which it is recycled or is disposed as solid waste. The term...
expo for marijuana-related products from cannabis-oriented businesses. A DVD called High Times Presents: The Cannabis Cup was made after the 2003 festival...
Global Information